Two-affine cover of a smooth projective curve
= Two-affine cover of a smooth projective curve
A nonconstant rational function on a <smooth projective curve> extends to a <finite morphism> to the <projective line>. The inverse images of its two standard affine charts are <affine varieties> covering the curve. The resulting <Čech cochain complex> has only degrees zero and one, so every <coherent sheaf> has zero <sheaf cohomology> in degrees at least two.